R36 : means to game the Sharpe ratio returns, monthly, statements, single

DoubleDip

V5, p87, the two statements in the last paragraph :

1. Does it mean ?
Yearly SD < monthly SD x 12^1/2 < weekly x 12^1/2 < daily SD < 250^1/2 ?
SD : Standard Deviation, ^1/2 : Square Root

2. Does it mean ?
The mean return used in the numerator of the calculated Sharpe ration is resulted from
compounding 12 months returns while the Standard Deviation from a single month's
return (or the mean of 12 month returns) is used in the denominator ?

Anyone can advise ?

dyga

1. By lengthening the measurement interval - std deviation increases.

Usually annual std dev > weekly std dev.
But what is a way this number can be gamed?
if you calculated a weekly std deviation and converted it into a annual std deviation using
annual std dev calculated = weekly std dev * sqrt(52) (since there are 52 weeks in a year) the annual calculated std dev will be a smaller number.

but numerator likewise would not be affected. It would be more or less the same number (r weekly * 52 would be approximately equal to r-annual.)

but now since a lower annual std dev calculated is used - the sharpe ratio now would be a HIGHER number (since the denom. is lower).

2:
Returns are compounded. So numerator = (1+rweek1)*(1+rweek2)*...(1+rweek52) - 1
std dev = monthly std dev*sqrt(12). (not compounded).

return would most likely be equivalent to the annual return (or off by a very little bit).
but std deviation calculated as above would be lower - so end result Sharpe Ratio would be higher.

CP

bodhisattva

CP, thank you very much for your response !

1. What you meant are :
Acutually (usually) : Yearly SD > monthly SD > weekly SD > daily SD
if the Yearly SD is calculated as : monthly SD x 12^1/2 or weekly SD x 52^1/2 or
daily SD x 250^1/2, the calculated Yearly SD will be lower than the actual yearly SD,
i.e., the calculated yearly SD is an under-estimated one and the calculated Sharpe ratio
will be HIGHER than the actual/real one.
Am I right ?

2. In your example, I think the return in the numerator shall be : (1+r month1)*
(1+r Month 2) * ...(1+r month 12) -1 , since you use "monthly" SD in the denomintor.
What is the monthly SD here ? The SD of a specific single month's return ?
And this will lead to higher Sharpe ratio (than real one) ?
Since sqrt(12) = 3.464 and the annualized yearly return (compounded from monthly
returns) is not necessarily 3.464x greater than the annualized yearly return, therefore,
I think it is not necessarily that the calculated Sharpe ratio will be HIGHER than the
actual/real one. i.e., there is a likelyhood that the the calculated Sharpe ratio will be
LOWER than the actual/real one. But in any case, the calculated Sharpe ratio will be a
distorted one.
Am I correct ?

pennyless

I come back to this issue because I still can't get it. Anyone can help ?

ll11

AMA technical you may be but darn it you overthink everything .............................returns are linked geometically while standard deviation is a function of sqrt(T)



"Simplify as much as possible, but no further."

my boi Bert

Unforseen

1) It may simply mean that SD(based on annual return) < SD(based on monthly return) and etc.
It's the "smoothing", I think.

2) I also have a difficulty in understanding it. It is more a general problem than specific to Sharpe ratio.

SD(based on monthly return) = SD_M x sqrt(12)
R > Sum(12 monthly return)=Avg(monthly return)*12. It could be "<" in a bear market due to compounding.

But we usually use avg(monthly return) in SD calculation....kind of inconsistent.

PS. R and SD here are annualized.



Edited 1 time(s). Last edit at Monday, April 4, 2011 at 10:43AM by deriv108.

NakedPuts00

1) is a gaming.
2) is more like a problem of Sharpe Ratio itself. If not calculating that way, what else can we do?

former

pimpineasy Wrote:
-------------------------------------------------------
> AMA technical you may be but darn it you overthink everything .............................returns
> are linked geometically while standard deviation is a function of sqrt(T)
>
> "Simplify as much as possible, but no further."
>
> my boi Bert

This forum is open for discussions of any issue in the curriculum !

Roflnadal

alta
since you dont understand me i think u stand under me .......................


never meant it as a dis or a dont discuss this topic ................all i was pointing out is that AMA has a tendency to overthink things when a much simpler approach would be more elegant



Edited 1 time(s). Last edit at Monday, April 4, 2011 at 11:28AM by pimpineasy.

bboo

pimpineasy Wrote:
-------------------------------------------------------
> alta
> since you dont understand me i think u stand under me .......................
>
> never meant it as a dis or a dont discuss this topic ................all i was pointing out is
> that AMA has a tendency to overthink things when a much simpler approach would be more > elegant

I don't think he is overthinking, you can see here other candidates have same questions (including me). It good to raise question here and get clarification through discussions.